1)How many ways can the letters in the word BOOKKEEPER be arranged? (Must show set-up )

2)Seven swimmers compete in the championship freestyle 50m race. How many ways can first, second, and third place prizes be awarded? You must show your set-up

3) Katie has a bag of candy consisting of 9 red gumdrops, 15 orange gumdrops, and 7 green gumdrops. If she eats 2 of the gumdrops one after the other, what is the probability that the following will occur? Reduce all fractions.

A) The first candy eaten was orange and the second one was red:

B) Both gumdrops were green in color:

Question

25-05-2017
Mathematics

contestada

1)How many ways can the letters in the word BOOKKEEPER be arranged? (Must show set-up )

2)Seven swimmers compete in the championship freestyle 50m race. How many ways can first, second, and third place prizes be awarded? You must show your set-up

3) Katie has a bag of candy consisting of 9 red gumdrops, 15 orange gumdrops, and 7 green gumdrops. If she eats 2 of the gumdrops one after the other, what is the probability that the following will occur? Reduce all fractions.

A) The first candy eaten was orange and the second one was red:

B) Both gumdrops were green in color:

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Question 1

There are 5 letters (B, O, K, E, R) and there is a total of 10 letters to make up the word.
There are [tex] \frac{10!}{(10-6)!6!} [/tex] ways of arranging the letters, which equal to 210 ways

Question 2

There are seven swimmers in total.
There are [tex] \frac{7!}{(7-1)!1!} [/tex] ways of choosing the first winner, which is 7 ways
There are [tex] \frac{6!}{(6-1)!1!} [/tex] ways of choosing the second winner, which is 6 ways
There are [tex] \frac{5!}{(5-1)!1!} [/tex] ways of choosing the third winner, which is 5 ways
There are 7×6×5=210 ways of choosing first, second, and third winner

Question 3

The probability of eating an orange and a red candy is [tex] \frac{15}{31} [/tex]×[tex] \frac{9}{30} [/tex], which equals to [tex] \frac{9}{62} [/tex]

The probability of eating two green candies is [tex] \frac{7}{31} [/tex]×[tex] \frac{6}{30} [/tex] which equals to [tex] \frac{7}{155} [/tex]